LDPC Parity-Check Matrix Layout Using Cyclic Shifted Identity Blocks
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Solution Overview
Problem
Current methods for constructing Low Density Parity Check (LDPC) codes lack flexibility, making it difficult to design codes for various communication systems that require near-capacity achieving error correction and improved Bit Error Rate (BER) performance across different Signal to Noise Ratios (SNR).
Innovation Solution
The use of Cyclic Shifted Identity (CSI) sub-matrices in the parity check matrix of LDPC codes, allowing for the construction of both regular and irregular LDPC codes with reduced complexity and improved hardware implementation, enables the design of LDPC codes that approach the Shannon limit and offer better error correction performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional LDPC code construction methods are used, then code design is straightforward, but flexibility and adaptability to different communication systems are limited
Solution Approach 1:
The parity check matrix is segmented into multiple sub-matrices, each corresponding to a specific codeword of the Reed-Solomon code. This segmentation allows independent design and optimization of each sub-matrix while maintaining the overall code structure, thereby increasing flexibility without proportionally increasing complexity.
Solution Approach 2:
The patent employs Reed-Solomon codes as a universal foundation for constructing LDPC codes. The same Reed-Solomon code framework can generate different LDPC code ensembles by varying the parity check matrix construction parameters, providing multi-functionality and adaptability across different communication system requirements.
2Reliability
If LDPC codes are designed to approach the Shannon limit, then error correction performance is improved, but hardware implementation complexity increases
Solution Approach 1:
The patent varies parameters such as the Reed-Solomon code length, dimension, and parity check matrix construction parameters to optimize the balance between error correction performance and hardware complexity. By adjusting these parameters, codes can be designed to approach the Shannon limit while maintaining practical hardware implementability.
3Reliability
If irregular LDPC codes are constructed for better BER performance, then error correction capability is improved, but code construction complexity increases
Solution Approach 1:
The patent introduces irregularity in the LDPC code construction by applying different operations to different sub-matrices of the parity check matrix. Specifically, some sub-matrices are constructed using addition operations while others use multiplication operations, creating local variations in code properties that improve BER performance without requiring complete redesign of the entire code structure.
Data Source
AI summary
Algebraic method to construct LDPC (Low Density Parity Check) codes with parity check matrix having CSI (Cyclic Shifted Identity) sub-matrices. A novel approach is presented by which identity sub-matrices undergo cyclic shifting, thereby generating CSI sub-matrices that are arranged forming a parity check matrix of an LDPC code. The parity check matrix of the LDPC code may correspond to a regular LDPC code, or the parity check matrix of the LDPC code may undergo further modification to transform it to that of an irregular LDPC code. The parity check matrix of the LDPC code may be partitioned into 2 sub-matrices such that one of these 2 sub-matrices is transformed to be a block dual diagonal matrix; the other of these 2 sub-matrices may be modified using a variety of means, including the density evolution approach, to ensure the desired bit and check degrees of the irregular LDPC code.